Measuring the Strangeness Content of the Nucleon by Observing the ϕ-Meson Mass Shift in Nuclear Matter

Abstract

Light vector mesons at finite density have been studied already for quite some time. They have attracted much interest especially because the vector mesons have the potential to carry information on the partial restoration of chiral symmetry in nuclear matter, which could be measured in experiments [1, 2]. The early works studying QCD sum rules for the vector channels at finite density [1, 3] therefore provided strong incentives for later experiments. Things have however turned out to be a bit more complicated than they were thought to be. Even though QCD sum rules indeed provide some relation between the spectral function of the various vector channels and the order parameters of chiral symmetry, this relation is not a direct one for the ρ and ω as the driving term for the modification of the spectrum entering into the sum rules contains not the simplest two-quark condensate but the less known four-quark condensate. Furthermore, the change of the spectral function should not be considered to be a simple mass shift of the ground state peak, but rather a combination of mass shift and some sort of broadening for which the sum rules give only a weak constraint [4]. For the φ, these issues are less severe because the sum rule input depends much less on the four-quark condensate and its broadening at nuclear matter density has been estimated to be well below 100 MeV [5]. We will therefore concentrate our efforts on the φ-meson in this work [6]. In this channel the most important quantity which determines the modification of the spectral function at finite density is the strangeness content of the nucleon, 〈N|ss|N〉, which governs, in the linear density approximation, the behavior of the strange quark condensate: